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Let $G$ be a finite group. In [Ghasemabadi et al., characterizations of the simple group ${}^2D_n(3)$ by prime graph and spectrum, Monatsh Math., 2011] it is proved that if $n$ is odd, then ${}^2D _n(3)$ is recognizable by prime graph and also by element orders. In this paper we prove that if $n$ is even, then $D={}^2D_{n}(3)$ is quasirecognizable by prime graph, i.e. every finite group $G$ with $Gamma(G)=Gamma(D)$ has a unique nonabelian composition factor and this factor is isomorphic to $D$.